Recoil scheme and logarithmic accuracy in agular-ordered parton showers Silvia Ferrario Ravasio IPPP Durham Milan Christmas Meeting 19-20 December 2019 Based on Gavin Bewick, S.F.R., Peter Richardson and Mike Seymour [arxiv:1904.11866] Silvia Ferrario Ravasio — December 20 th , 2019 1/28 Recoil effects in angular-ordered PS
Introduction: Shower Monte Carlo generators Shower Monte Carlo (SMC) event generators can simulate fully realistic collider events, being able to reproduce much of the data from LHC and its predecessors at high accuracy. Silvia Ferrario Ravasio — December 20 th , 2019 2/28 Recoil effects in angular-ordered PS
Introduction: Shower Monte Carlo generators Shower Monte Carlo (SMC) event generators can simulate fully realistic collider events, being able to reproduce much of the data from LHC and its predecessors at high accuracy. The core of SMC is given by the Parton Shower. Silvia Ferrario Ravasio — December 20 th , 2019 2/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (I) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � ( | � p | cos θ pk ) k | Silvia Ferrario Ravasio — December 20 th , 2019 3/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (I) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � ( | � p | cos θ pk ) k | in the (quasi-) collinear limit, the cross-section factorizes: dσ n +1 ( Q ) = dσ n ( Q ) α s ij → i,j ( z ) dt dφ where t = { p 2 T , q 2 ij , E 2 θ 2 , . . . } 2 π P ˜ ˜ t 2 π Silvia Ferrario Ravasio — December 20 th , 2019 3/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (I) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � ( | � p | cos θ pk ) k | in the (quasi-) collinear limit, the cross-section factorizes: dσ n +1 ( Q ) = dσ n ( Q ) α s ij → i,j ( z ) dt dφ where t = { p 2 T , q 2 ij , E 2 θ 2 , . . . } 2 π P ˜ ˜ t 2 π Factorization can be applied recursively: We define an ordering variable t : Q > t 1 > t 2 > t 3 > . . . > t cutoff ij → i,j ( t, z, φ ) = α s ij → i,j ( z, t ) dz dt dφ Emission probability dP ˜ 2 π P ˜ t 2 π Sudakov form factor � t i � z max ( t ′ ) � ij → i,j ( z, t ′ ) � P ˜ dz α s dt ′ ∆( t i , t i +1 ) = exp − 2 π t ′ t i +1 z min ( t ′ ) Silvia Ferrario Ravasio — December 20 th , 2019 3/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (II) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � k | ( | � p | cos θ pk ) Silvia Ferrario Ravasio — December 20 th , 2019 4/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (II) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � k | ( | � p | cos θ pk ) emission of n additional partons → at # logs most 2 n logs: leading log LO LL NLL p o w Silvia Ferrario Ravasio — December 20 th , 2019 4/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (II) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � k | ( | � p | cos θ pk ) emission of n additional partons → at # logs most 2 n logs: leading log LO LL (quasi-) collinear splitting functions NLL correctly describe all the LL (collinear AND soft) but only the collinear NLL . (1 − z ) 2 m 2 z → 1 P i,g ( z, t ) = 2 C i � � i lim 1 − (1 − z ) 2 m 2 i + | p 2 1 − z T | p o w Silvia Ferrario Ravasio — December 20 th , 2019 4/28 Recoil effects in angular-ordered PS
Parton Showers in a nutshell (II) When a (quasi) collinear parton or a soft gluon is emitted, we have a logarithmic divergence: ∝ d | � ( p + k ) 2 − m 2 = d | � dσ n +1 k | d cos θ pk k | d cos θ pk p | 2 + m 2 − | � | � dσ n � k | ( | � p | cos θ pk ) emission of n additional partons → at # logs most 2 n logs: leading log LO LL (quasi-) collinear splitting functions NLL correctly describe all the LL (collinear AND soft) but only the collinear NLL . (1 − z ) 2 m 2 z → 1 P i,g ( z, t ) = 2 C i � � i lim 1 − (1 − z ) 2 m 2 i + | p 2 1 − z T | p o w � �� 1 + α MS 18 − π 2 ( p T ) �� 67 � C A − 5 α s = α CMW ( p T ) = α MS s ( p T ) 9 n f s s 2 π 6 allows to mimic all LL and NLL , except for those due to soft wide angle gluon emissions. Silvia Ferrario Ravasio — December 20 th , 2019 4/28 Recoil effects in angular-ordered PS
which is the logharitmic accuracy of parton showers? The naive expectation is that parton showers are LL accurate, almost NLL. From Pythia manual: “While the final product is still not certified fully to comply with a NLO/NLL standard, it is well above the level of an unsophisticated LO/LL analytic calculation.” From Bewick etal. (v2) “In general defining a strict logarithmic accuracy for a parton shower algorithm is difficult. Formally the parton shower is only accurate at leading, or double logarithmic, accuracy. However, a number of phenomenologically important, but formally subleading effects are included.” Silvia Ferrario Ravasio — December 20 th , 2019 5/28 Recoil effects in angular-ordered PS
which is the logharitmic accuracy of parton showers? The naive expectation is that parton showers are LL accurate, almost NLL. From Pythia manual: “While the final product is still not certified fully to comply with a NLO/NLL standard, it is well above the level of an unsophisticated LO/LL analytic calculation.” From Bewick etal. (v2) “In general defining a strict logarithmic accuracy for a parton shower algorithm is difficult. Formally the parton shower is only accurate at leading, or double logarithmic, accuracy. However, a number of phenomenologically important, but formally subleading effects are included.” Need for a framework where evaluate the accuracy of a PS: Silvia Ferrario Ravasio — December 20 th , 2019 5/28 Recoil effects in angular-ordered PS
which is the logharitmic accuracy of parton showers? The naive expectation is that parton showers are LL accurate, almost NLL. From Pythia manual: “While the final product is still not certified fully to comply with a NLO/NLL standard, it is well above the level of an unsophisticated LO/LL analytic calculation.” From Bewick etal. (v2) “In general defining a strict logarithmic accuracy for a parton shower algorithm is difficult. Formally the parton shower is only accurate at leading, or double logarithmic, accuracy. However, a number of phenomenologically important, but formally subleading effects are included.” Need for a framework where evaluate the accuracy of a PS: Logharitmic accuracy of parton showers: a fixed-order study , by Dasgupta, Dreyer, Hamilton, Monni and Salam, introduced approach for assessing the logarithmic accuracy of PS algorithms based on the ability to reproduce: 1 the singularity structure of multi-parton matrix elements 2 logarithmic resummation results Silvia Ferrario Ravasio — December 20 th , 2019 5/28 Recoil effects in angular-ordered PS
Logharitmic accuracy of parton showers: a fixed-order study (I) Case of study: double gluon emission, well separated in rapidity, in e + e − → q ¯ q (all massless): 2 dP 2 = C 2 2 α s ( p T,i ) dp T,i � � θ �� � F dη i where η i = − log tan 2! π p T,i 2 i =1 Silvia Ferrario Ravasio — December 20 th , 2019 6/28 Recoil effects in angular-ordered PS
Logharitmic accuracy of parton showers: a fixed-order study (I) Case of study: double gluon emission, well separated in rapidity, in e + e − → q ¯ q (all massless): 2 dP 2 = C 2 2 α s ( p T,i ) dp T,i � � θ �� � F dη i where η i = − log tan 2! π p T,i 2 i =1 Dipole showers implemented in the Pythia8 and Sherpa generators were considered. colour structure Silvia Ferrario Ravasio — December 20 th , 2019 6/28 Recoil effects in angular-ordered PS
Logharitmic accuracy of parton showers: a fixed-order study (II) Issue with dipole showers Dipole frame: there are region where the second gluon looks ¯ q = emitter g = emitter closer to the first gluon When the gluon is identified as emitter: � p T, 1 → � p T, 1 − � p T, 2 1 2 Wrong colour C A g = emitter q = emitter instead of 2 C F (subleading N c ). Silvia Ferrario Ravasio — December 20 th , 2019 7/28 Recoil effects in angular-ordered PS
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